Modelo para o cálculo de tensões biaxial e triaxial em materiais ortotrópicos: análise da coerência das equações para um filme fino transversalmente isotrópio de ouro

Abstract

In this work an analytical model based on the theory of elasticity was proposed to measure the residual stress in orthotropic materials has been described and applied to evaluate the Poisson's ratio thin lms of gold. The metallic materials generally have anisotropy in addition the crystallographic texture, which causes problems to analyze the stress making use X-ray di raction , since the 𝜀 vs sin2 𝜓 curves become nonlinear. Applying the symmetries from the material in the orthotropic elastic tension was obtained stress-strain relations for orthotropic material, the equations for deformations were found in accordance with the state of triaxial and biaxial principal stresses for the case where the deformations are calculated via XRD. A new equation was proposed for the Poisson coe cient out of the plane in the case of thin lms transversely isotropic. A speci c case was done by applying the equations to the experimental data in the literature for a thin lm of gold with ber texture {111}, so the value of the Poisson coe cient out of the plane could be calculated in two methods. The rst was performed by tting the experimental data by the least squares method. The second the Poisson coe cient was calculated as an average value on the surface, which was built for the Poisson coe cient out of the plane as a function of sin2 𝜓 and 𝜀.